How do you react to a perceived threat? Fight or flight is what covers most automatic responses. Stopping and having a think about it doesn’t have the same positive vibe but in the case of discovering that another email marketing company has undercut your price for a product it is the most logical way to go.
You will have, no doubt, exercised a great deal of care in coming to the decision as to what to charge. If someone else charges a lot lower then there must be a reason. However, it might not be one that you need to respond to.
The company that has set your heart pumping might have any number of reasons for their tactic. If they are a newcomer then they will probably be after building both their client list and their email marketing list. A loss leader might make sense to them but it is a short term ploy.
The same goes for a company that is struggling for some reason. You might sympathise with those who have problems with cash flow but know that selling cheap is not a long term solution. A failing company realising its assets may cost you, but a knee jerk reaction is for jerks.
An email marketing campaign that dropped into my inbox showed slashed prices for software. The company was abandoning the lines so they did not only get some cash but hurt their competitors into the bargain. Great tactics.
The problem for you is that there could be a number of reasons and there are a number of responses that might be the best option for you. The only way to win any war, price or otherwise, is not to take part and this should be the default position for you until there is evidence to show you need to respond and in what manner.
The worst option is that the company is expanding into your field after being successful in others. You will, sensibly, be concerned, but now is not the time to eat into your reserves. You might need them later.
Acting immediately gives the feeling of maintaining control, but you want sensible, not automatic, responses.